PRP Records

Probable Primes Top 10000

(201620 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
90015^76654-2653579Lelio R Paula10/2012
9002(3^112297-2)/762753576Lelio R Paula03/2012
90033*2^177948-753569Lelio R Paula03/2014
900410^53558+1854353559Patrick De Geest12/2012
900510^53558-2153558Robert Price03/2011
90062^177792-9553521Lelio R Paula02/2011
900713392^9919+9919^1339253521Hans Havermann07/2016
900813105^12132+12132^1310553520Hans Havermann07/2016
900913^48042+8253517Lelio R Paula01/2013
90102^177768+3912153514Yves Minet10/2010
901113835^7366+7366^1383553504Hans Havermann07/2016
901217^43477+8453497Lelio R Paula01/2013
90135*10^53492+953493Dmitry Domanov11/2010
90142^177683+9553488Lelio R Paula01/2011
901511057^13226-13226^1105753482Norbert Schneider12/2017
9016(2^177678+3)/51462753481Lelio R Paula02/2012
90172^177641-25546353476Gary Barnes08/2009
9018p(11608)#/2+1653469Robert Price12/2016
9019(14*10^53465+211)/953466Robert Price11/2017
902037302#*10^(37302+52)+p(37302+1)53457Jason Earls08/2008
902112001^13104-13104^1200153455Norbert Schneider10/2017
90221829^16384+1828^1638453449Henri Lifchitz01/2007
902335^34608-960253438Enzo Doria03/2013
9024(3^111992+8)/1486753430Lelio R Paula03/2012
90262^177480+186966153427Enzo Doria05/2016
902511791^13122-13122^1179153427Norbert Schneider10/2017
9027(8*10^53411+1)/953411Serge Batalov12/2008
90284*5^76410-353409Lelio R Paula09/2014
90292^177380-11304553397Enzo Doria07/2014
90305^76362-2*3^7636253375Mike Oakes11/2009
90314159^14747-14053370Enzo Doria07/2012
9032(lucasV(1,2,354503)-2)/353358Mike Oakes03/2017
9033p(11586)#/2+3253357Robert Price12/2016
903415^45362-4653350Lelio R Paula01/2013
903514147^5892+5892^1414753338Hans Havermann07/2016
90367^63109+4653334Lelio R Paula10/2012
903720^40986-134353325Enzo Doria03/2013
90384*10^53324-8953325Robert Price08/2017
903920^40977-888353313Enzo Doria03/2013
90403^111711+266053300Lelio R Paula10/2012
90412^177040-1186553295Enzo Doria10/2012
9042(7*10^53287+17)/353288Erik Branger03/2014
904335^34506-1075853280Enzo Doria03/2013
9044(11*10^53274-17)/353275Erik Branger03/2014
9045(1017*2^176971-1)/33553275Lelio R Paula03/2015
90462^176961-283353271Yves Minet09/2014
90473^111642+11053267Lelio R Paula10/2012
904817^43290-9853267Lelio R Paula01/2013
90497^63028+3653265Lelio R Paula10/2012
9050(22*10^53264+71)/353265Robert Price05/2017
90517^63023-3653261Lelio R Paula10/2012
905219783^492+492^1978353256Anatoly F. Selevich02/2007
905313350^9739+9739^1335053247Hans Havermann10/2015
905414394^4993+4993^1439453235Hans Havermann10/2015
90552^176823-11280753230Enzo Doria06/2014
90561684^16495+16495^168453219Serge Batalov05/2014
905715277^3042+3042^1527753213Hans Havermann06/2016
9058(50322^11317-1)/5032153206Serge Batalov04/2015
90592^176742-159553205Lelio R Paula10/2009
9060(27*2^176767-1)/2045505635553204Lelio R Paula01/2014
9061(-lucasV(1,2,353460)-2)/(3^2*5^2)53199Mike Oakes03/2017
9062(3*2^176696-1)/29953189Lelio R Paula01/2014
9063(7*10^53185-1)/353186Erik Branger03/2014
90642^176629+46553171Lelio R Paula07/2012
9065(3*2^176604-1)/35953162Lelio R Paula01/2014
906610955^13158-13158^1095553154Norbert Schneider11/2017
90675^76038-1436653149Enzo Doria02/2013
906815156^3209+3209^1515653143Hans Havermann06/2016
90692^176532-283753142Yves Minet09/2014
907052^30967-5153140Norbert Schneider08/2014
90719*5^76023-253139Lelio R Paula09/2014
9072(14283!+1)/46421617753135Michael Porter03/2016
90732^176461-16553121Lelio R Paula02/2011
9074(62*10^53111+1)/953112Serge Batalov05/2010
90752^176403-13953103Lelio R Paula02/2011
907655^30508-253095Lelio R Paula08/2013
9077(48591^11329-1)/4859053090Serge Batalov04/2015
90783^111254-8853082Lelio R Paula10/2012
907915^45129-5653076Lelio R Paula01/2013
90802^176293-7353070Lelio R Paula01/2011
9081(67*10^53068+41)/953069Robert Price09/2015
908215271^2986+2986^1527153069Hans Havermann06/2016
90832^176255-66753059Yves Minet01/2012
908436471*2^176221+864753053Paul Vanderveen04/2016
9085(19*10^53049-1)/953050Serge Batalov03/2009
90869*2^176203-553044Lelio R Paula03/2014
90872^176205-9439553043Lelio R Paula08/2011
9088(19*2^176224-1)/21791691353042Lelio R Paula01/2014
908917^43103+1453037Lelio R Paula01/2013
9090(31*2^176188-1)/355553036Lelio R Paula01/2014
90912^176177+6094753035David Broadhurst05/2002
9092(22*10^53033-7)/353034Erik Branger09/2014
909313810^6909+6909^1381053023Hans Havermann06/2016
90942^176108+1609553014Lelio R Paula10/2009
90952^176107+1891553014Lelio R Paula07/2012
90963^111080-962852999Enzo Doria02/2013
90972^176047-155152996Yves Minet08/2012
90982^176042+7351952994Enzo Doria04/2016
9099lucasV(1715,1,2^14)/6553752986Mike Oakes04/2009
91002^175984-11225952977Enzo Doria06/2014
910111^50870+1052976Lelio R Paula01/2013
9102(11*10^52956+19)/352957Robert Price03/2016
9103gcd(V(949965),5*F(189993)*(F(189993)+1)+1)52941Serge Batalov04/2015
9104(-lucasV(1,2,351735)+2)/(3*7*263)52938Mike Oakes03/2017
9105(98*10^52931-89)/9952931Ray Chandler11/2010
910613774^6963+6963^1377452931Hans Havermann06/2016
91072^175812-136752925Yves Minet05/2013
91082^175801+1155*17580152922Henri Lifchitz01/2005
910911^50801-909052904Enzo Doria02/2013
911043^32374+1252882Robert Price11/2013
91112^175628+1352870Lelio R Paula01/2011
91122^175615-174752866Yves Minet09/2012
9113(13*10^52861+107)/352862Robert Price11/2017
91149*2^175586-752858Lelio R Paula03/2014
911512174^12937+12937^1217452854Norbert Schneider04/2016
9116(15*2^175565+1)/835952848Lelio R Paula07/2012
9117(2^175631-1)/330463093135534238072561/9273316952839Robert Kinser03/2017
911814256^5077+5077^1425652828Hans Havermann06/2016
91192^175467+8287552821Lelio R Paula07/2012
9120(7*10^52819+167)/352820Robert Kinser10/2017
9121(67607*2^175426+1)/352813Lelio R Paula05/2014
912213^47400-6052801Lelio R Paula01/2013
91234*10^52792+6352793Robert Price06/2016
9125(78557*2^175360+1)/308752791Lelio R Paula06/2014
912418^42055-292952791Enzo Doria03/2013
91269*5^75521+252788Lelio R Paula09/2014
91276^67814+3152770Lelio R Paula10/2012
912870^28600+6952770Norbert Schneider10/2012
912914^46038+9752766Lelio R Paula01/2013
9130(61*10^52763-7)/952764Serge Batalov02/2009
91312*5^75474+952755Lelio R Paula09/2014
913210^52753+282643060952754Robert Price05/2015
913310^52753+18399752754Patrick De Geest01/2016
913410^52753-5015352753Patrick De Geest03/2016
913519846^455+455^1984652751Anatoly F. Selevich02/2007
91362^175217+7297752746Enzo Doria04/2016
9137p(11466)#/2-25652746Robert Price05/2017
9138(4*10^52740+41)/952740Robert Price11/2014
91392^175189+538552738Lelio R Paula08/2009
91402^175160+938552729Lelio R Paula07/2008
914112356^12885+12885^1235652724Norbert Schneider03/2016
91422^175137+1152722Lelio R Paula01/2011
914365^29077-64^2907752715Robert Price08/2013
91442*10^52713-8752714Robert Price06/2016
91452^175106-46552713Lelio R Paula08/2009
91462^175089-5869552708Lelio R Paula08/2009
91482^175045+19552694Lelio R Paula02/2011
9147195^23010-252694Lelio R Paula10/2017
91492^175025+14952688Lelio R Paula02/2011
9150(19^41201+1)/2052685Paul Bourdelais03/2010
9151(436*10^52683-13)/952685Robert Price10/2017
91522*12^48815-5^4881552681Mike Oakes10/2010
9153335^20862-20862^33552678Norbert Schneider09/2015
91542^174983-760552676Lelio R Paula07/2009
91554*10^52667+1952668Robert Price04/2016
9156(10^52667+77)/352667Robert Price01/2017
915711434^12977+12977^1143452664Norbert Schneider04/2016
91582^174941-120352663Lelio R Paula07/2009
91592^174910+1270552654Lelio R Paula07/2012
91603^110338+7452645Lelio R Paula10/2012
91615^75303+1252635Lelio R Paula10/2012
91622^174836+25525552631Lelio R Paula07/2009
9163(66^28921+1)/6752622Paul Bourdelais08/2017
916420^40443+952618Lelio R Paula01/2013
9165(11*2^174788+1)/952617Lelio R Paula01/2012
9166(11*2^174786-1)/70352615Lelio R Paula01/2014
916711^50520-129052612Enzo Doria11/2012
9168(10^52608-19)/952608Robert Price10/2017
9169(9913*2^174736-1)/33352603Lelio R Paula03/2015
917013145^10024+10024^1314552594Hans Havermann05/2016
91715003^14217-15052592Enzo Doria07/2012
917219^41123+1052587Lelio R Paula01/2013
91732^174683+1290952585Lelio R Paula01/2011
91742^174643+5952573Lelio R Paula01/2011
9175(1017*2^174640-1)/77352572Lelio R Paula03/2015
917613529^7662+7662^1352952552Hans Havermann06/2016
9177121421#+18876752548Makoto Morimoto02/2016
917820^40375-592352530Enzo Doria03/2013
9179(67607*2^174503+1)/9094807952528Lelio R Paula05/2014
9180(-lucasV(1,2,349014)+2)/(7*50873*1047043)52521Mike Oakes03/2017
91812^174462+34552519Lelio R Paula07/2009
9182t(178863)52509Robert Price10/2014
91832^174416+85552505Lelio R Paula07/2009
91846^67467-10352500Lelio R Paula10/2012
9185(2^174533-1)/(193594572654550537*91917886778031629891960890057)52494Dario Alpern06/2017
91862^174329-1126552479Enzo Doria06/2014
91872^174314-124152474Yves Minet05/2009
918952^30577-5152471Norbert Schneider08/2014
91889403^13206-13206^940352471Norbert Schneider12/2017
919015692^2205+2205^1569252465Hans Havermann06/2016
9191(2^174281-7)/62881702961552453Lelio R Paula02/2012
9192(2^174240+5)/352451Lelio R Paula02/2012
9193(86*10^52450-221)/952451Robert Price06/2017
9194(62*10^52448-197)/952449Robert Price10/2017
9195(15*2^174221+1)/40352445Lelio R Paula07/2012
919626313!2-3252443Robert Price10/2015
9197(3*2^174214-1)/374872952438Lelio R Paula01/2014
91982*3^109900-552436Lelio R Paula03/2014
92004159^14488-15052432Enzo Doria07/2012
9199(89*10^52431-71)/952432Robert Price11/2015
92012^174170-394152431Yves Minet04/2017
9202(7*2^174171-1)/68552429Lelio R Paula01/2014
9203(260137^9679+1)/26013852409Faysal YAtim03/2008
92042^174098+7952409Lelio R Paula01/2011
920535^33940-221452406Enzo Doria03/2013
920615^44557+252404Ray Chandler07/2011
92072^174049-43952394Yves Minet01/2012
92086^67329+11552393Lelio R Paula10/2012
92102^174041+26214552392Lelio R Paula07/2009
9209141^24377+252392Lelio R Paula05/2013
9211lucasU(285,1,21339)-lucasU(285,1,21338)52382Mike Oakes05/2009
92122^174001-595552380Lelio R Paula07/2009
9213lucasV(-1,2,347969)52375Mike Oakes02/2017
92143^109764-14052371Lelio R Paula10/2012
92162*3^109761+752370Lelio R Paula03/2014
92159863^13112-13112^986352370Norbert Schneider10/2017
92172^173944-11225352363Enzo Doria06/2014
92192^173940+111152362Lelio R Paula01/2011
9218(3126^14983-1)/312552362Richard Fischer03/2015
922015214^2763+2763^1521452358Hans Havermann05/2016
922113200^9247+9247^1320052352Hans Havermann05/2016
9222(1017*2^173867-1)/717552339Lelio R Paula03/2015
922313732^6465+6465^1373252327Hans Havermann05/2016
9224(2^173867-1)/5253663750268952326Donovan Johnson06/2005
92252^173811-68487752323Paul Bourdelais11/2012
92262^173807-595552322Lelio R Paula06/2009
92272^173796-104468952318Paul Bourdelais11/2012
922810^52317+6449752318Patrick De Geest12/2012
922910^52317+6474352318Patrick De Geest12/2012
923110^52317-7152317Robert Price05/2011
923010821^12968+12968^1082152317Norbert Schneider04/2016
9232(298*10^52308-7)/352310Robert Price06/2017
9233(2^173778-3)/5795952308Lelio R Paula02/2012
923410232^13043-13043^1023252302Norbert Schneider08/2017
92352^173727+952298Lelio R Paula01/2011
9236(14^45631+13^45631)/2752298Robert Price04/2013
923737856!3+656152293Robert Price11/2015
92384*3^109596+552292Lelio R Paula03/2014
923915436^2441+2441^1543652291Hans Havermann05/2016
924043^32005+2452280Robert Price11/2013
92412^173650-16552274Lelio R Paula02/2011
92424*10^52272+9352273Robert Price01/2017
924319^40873+8452267Lelio R Paula01/2013
92442^173621+424242952266Jason Earls09/2008
92459999^13064-13064^999952256Norbert Schneider09/2017
9246numbpart(46909^2-1)52247Serge Batalov04/2017
924714^45579-3152240Lelio R Paula01/2013
9248(10223*2^173518+1)/90352236Lelio R Paula05/2014
924920^40147-612352233Enzo Doria03/2013
92504^86754-3^(86754+1)52232Robert Price04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 21 2018 09:45 (Time in France)

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